Convex and Semi-Nonnegative Matrix Factorizations

By Chris H. Q. Ding, Tao Li, Michael I. Jordan. 2010

1,391 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Computer Vision and Pattern Recognition, Numerical Analysis

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Citations in the corpus

Joint Unsupervised Learning of Deep Representations and Image Clusters (2016, background): “Related ideas form the basis of a number of methods, such as expectation maximization (EM) [7, 37], spectral clustering [40, 47, 61], and non-negative matrix factorization (NMF) based clustering [1, 8, 60].”
TaSNet: Time-Domain Audio Separation Network for Real-Time, Single-Channel Speech Separation (2017, methodology): “This signal factorization technique shares the motivation behind independent component analysis (ICA) with nonnegative mixing matrix [15] and semi-nonnegative matrix factorization (NMF) [16].”
UNKs Everywhere: Adapting Multilingual Language Models to New Scripts (2020, methodology): “For the latter, we have proposed a new method of encoding the embedding matrix into lower dimensional embeddings and a shared up-projection via Semi-NMF.”
Cross-Domain Recommendation via Cluster-Level Latent Factor Model (2013, background): “The proof could be refereed to [8] [9] for more details.”
Factorized Variational Autoencoders for Modeling Audience Reactions to Movies (2017, background): “In many applications, one or both of the factorized representations are constrained to be non-negative, which leads to non-negative MF [8, 27].”
Unsupervised sentiment analysis with emotional signals (2013, neutral): “Let ΓU = Γ + U−ΓU , where Γ+U (i, j) = (|ΓU (i, j)|+ΓU (i, j))/2 and ΓU (i, j) = (|ΓU (i, j)| − ΓU (i, j))/2 [7], we get [−(XVH + λI GU0 + λCWU + UΓU ) + (UHV VH + λI G U + λCD U + UΓ+U )](i, j)U(i, j) = 0.”
Algorithms for Nonnegative Matrix Factorization with the β-Divergence (2010, methodology): “gif" mimetype="image" xlink:type="simple"> is added to the criterion function) and convex NMF (when the dictionary is assumed to belong to a known subspace, as proposed by Ding, Li, and Jordan, 2010 ).”
The Why and How of Nonnegative Matrix Factorization (2014, methodology): “• Convex NMF [36], and the CUR decomposition [91].”
Collaborative matrix factorization with multiple similarities for predicting drug-target interactions (2013, background): “Another series of related work are “non-negative” matrix factorization (NMF) [6, 7], in which factorized matrices must keep the elements nonnegative.”
Non-negative Matrix Factorization on Manifold (2008, methodology): “Ding et al. [10] proposed a semi-NMF approach which relaxes the nonnegative constraint on U.”
Making machine learning models interpretable (2012, methodology): “An example of this is the application of semi-supervised blind signal separation, for instance with convex-NMF [42], which is reported elsewhere [43].”
A Survey on Knowledge Graph-Based Recommender Systems (2020, methodology): “Then L reﬁned latent vectors of users and items in different meta-paths can be obtained via applying the non-negative matrix factorization technique [109] on these diffused user preference matrices, Finally, the recommendation can be generated by combining the user’s preference on each path, with…”
Cross-language web page classification via dual knowledge transfer using nonnegative matrix tri-factorization (2011, methodology): “NMF is a useful learning method to approximate a nonnegative input data matrix by the product of factor matrices [11,12], which has been applied to solve many real world problems including dimensionality reduction, pattern recognition, clustering and classification [3,5–8,13,14,22,25].”
Nonnegative Matrix Factorization: A Comprehensive Review (2013, methodology): “Further more, Semi-NMF applies equally to the foregoing Convex NMF model [67].”
Archetypal analysis for machine learning (2010, neutral): “Thus AA accounts for more variation than K -means but less than SVD / PCA and NMF as indicated in Table 1, while the distinct facial aspects are ef-ﬁciently extracted.”
An Efficient Non-Negative Matrix-Factorization-Based Approach to Collaborative Filtering for Recommender Systems (2014, background): “It is initially designed for learning part-based object representations in computer vision [25], [26], [31], [32]; and then applied to CF problems [27]–[30].”
Robust (Semi) Nonnegative Graph Embedding (2014, background): “One line of approaches is to explicitly impose sparseness constraints, expecting more sparse representation than the original NMF [3], [16]–[18].”